How can I apply a different material during / after using "Solidify" modifier?
Your question is not clear enough, but if you want to keep the Solidify modifier (and not Apply it) and give the inner faces a different material, you need to go in the Solidify modifier and use the Material Index Offset, left value to set the color of the outer surface, right value for the color of the inner faces, 0 will mean it will use the first material of your material stack, 1 for the second material of your material stack, and so on.